Equation 677 Database

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Magma 6378847aa019…

magma 6378847aa019
Size
705
Isomorphism class hash
6378847aa019606fd1fea7f75a029d50deae42787d71400504a0d5000ffd9ccd
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 19:10:38
Display reorder
660,352,157,147,364,188,350,189,155,148,362,156,190,351,146,363,153,355,191,150,367,154,353,192,151,365,193,354,152,149,366,145,163,347,194,359,161,348,195,143,360,162,349,196,144,361,346,159,197,141,358,344,160,198,142,356,345,158,199,140,357,674,675,673,682,43,16,316,388,128,44,129,17,314,386,15,130,42,315,387,12,46,131,319,391,13,47,132,317,389,133,45,14,318,390,311,22,41,134,383,23,39,135,312,384,21,40,136,313,385,37,18,137,310,382,38,19,138,308,380,36,20,139,309,381,662,666,671,669,98,90,564,488,9,96,10,91,562,486,92,11,97,563,487,93,101,8,567,491,94,99,6,565,489,7,100,95,566,490,559,88,104,1,483,89,102,0,560,484,87,103,2,561,485,107,84,3,558,482,105,85,4,556,480,106,86,5,557,481,687,681,676,684,630,629,634,633,80,614,78,612,618,617,620,79,622,626,625,652,654,83,658,657,636,638,81,642,641,82,646,644,650,649,594,589,590,75,593,597,598,76,602,601,604,606,77,610,609,582,581,74,585,584,113,110,72,552,467,112,111,73,553,466,704,699,702,703,412,168,208,512,71,410,69,169,206,510,167,70,411,207,511,164,415,67,211,515,165,413,68,209,513,66,414,166,210,514,203,174,407,62,507,175,408,60,204,508,173,409,61,205,509,406,170,65,202,506,404,171,63,200,504,405,172,64,201,505,689,691,690,693,376,27,328,340,261,374,262,28,326,338,29,260,375,327,339,26,379,264,331,343,24,377,265,329,341,263,378,25,330,342,323,33,371,267,335,34,372,268,324,336,35,373,266,325,337,370,32,270,322,334,368,30,271,320,332,369,31,269,321,333,663,664,665,661,233,294,536,239,440,234,441,295,534,240,293,442,235,535,241,290,232,443,539,238,291,230,444,537,236,445,231,292,538,237,531,285,224,446,245,286,225,447,532,246,284,226,448,533,247,227,288,449,530,244,228,289,450,528,242,229,287,451,529,243,692,695,696,694,462,436,476,576,254,460,255,434,474,574,435,256,461,475,575,439,465,257,479,579,437,463,258,477,577,259,464,438,478,578,471,431,457,252,571,432,458,253,472,572,433,459,251,473,573,456,430,248,470,570,454,428,249,468,568,455,429,250,469,569,680,688,679,677,632,635,628,631,301,616,299,619,613,615,627,300,624,621,623,659,656,297,653,655,643,640,298,637,639,296,648,651,645,647,588,595,592,307,591,603,600,305,596,599,611,608,306,605,607,586,587,303,580,583,453,554,304,108,127,452,555,302,109,126,700,698,697,701,55,424,400,500,121,56,122,422,398,498,423,120,54,399,499,427,58,124,403,503,425,59,125,401,501,123,57,426,402,502,395,419,53,119,495,420,51,117,396,496,421,52,118,397,497,49,418,115,394,494,50,416,116,392,492,48,417,114,393,493,667,670,672,668,282,524,212,548,176,283,177,522,213,546,523,178,281,214,547,527,278,179,215,551,525,279,180,216,549,181,280,526,217,550,218,519,273,182,543,520,274,183,219,544,521,272,184,220,545,276,518,185,221,542,277,516,186,222,540,275,517,187,223,541,678,685,686,683 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#8e5759f62ba231b7a190308c910bac46805bb85b5237b53b53611999ba1c2d7b, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 19:10:38 · history